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Question:

The area (in sq. units) of the parallelogram whose diagonals are along the vectors 8^i - 6^j and 3^i + 4^j - 2^k, is.

65

52

26

20

Solution:

The correct option is A
65
→d1 × →d2 = |^i ^j ^k
8 -6 0
3 4 -2|
= 72^i -(-16)^j + 50^k
|→d1 × →d2| = √5184 + 9216 + 2500 = √16900 = 130
Area = 1/2|→d1 × →d2| = 1/2 × 130 = 65.